Question

I need help solving this problem...can you show me how to create the depreciation table?

For a given building that is currently in the design phase, a conventional HVAC system would cost $225,000 to purchase and install and have average annual operating costs of $22,000 per year over the building’s 30-year life, assuming no price increases in natural gas and electricity.  The system requires major maintenance at the end of Year 10 and Year 20 at a cost of $15,000 each time.

The alternative to the conventional HVAC system proposed by a green building consultant would require upgraded windows, more insulation, slightly different entry configurations but a much smaller HVAC system.  The initial cost of the required upgrades, design changes and equipment would be $300,000.  The annual operating costs for this system would average $10,000 per year over the building’s 30-year life, assuming no price increases in natural gas and electricity.  The system requires major maintenance at the end of Year 10 and Year 20 at a cost of $4,000 each time.

For both systems, all of the operating and major maintenance costs are tax-deductible.  

With either system the initial investment would be depreciated over 10 years using the straight-line method to zero salvage value.  At the end of 30 years the scrap value of either system would be $5,000.  The tax rate to apply to this analysis is 30% and the discount rate is 8%.  Again, all operating and maintenance expenses are tax deductible.

Assume that the company has enough income to take full advantage of all tax shields.

A.  Which system provides the lowest overall cost?  Compute the present value of the total lifetime cost of each system.  In terms of today’s dollars (i.e., present value) how much does the low-cost system save over the alternative?

B.  If natural gas and electricity prices rise, how would this effect the difference between the total costs of the two systems? Specifically, consider a 1% per year increase in energy prices (Assume all operating costs are for energy to simplify things).  How will this change the difference in the NPVs of these competing systems?

C.  If the discount rate was higher, how would this effect the difference between the total costs of the two systems?  You can answer in a single sentence.  It is not necessary to show any quantitative work.

Answer 1

Proposals	Conventional HVAC system	Modified HVAC System
Initial Cost	225,000	300,000
Annual Operating costs for 30 years	22,000	10,000
Maintenance @ year 10 & year 20 each	15,000	4,000
Scrap Value @ 30 year end	5,000	5,000
Yearly Depreciation over 10 years using SLM method	22,500	30,000
Tax rate	30%	30%
Tax savings p.a @ 30% of Depreciation amount for 10 year period. This will be inflow for the company	6,750	9,000
Discount Rate	8%	8%

a) Based on details given below is the computation of PV

The initial Costs, annual operating expenses, Maintenance costs are all cash outflows for each of the systems. Scrap value is an inflow at the end of 30 years. On yearly depreciation till 10 years, company will be able to save tax outflow to the extent of 30% on depreciation amount. This shall be considered as cash outflow and deducted from the total outflows.

a) Present Value computation of total life time costs of each proposal.

PV of Life time costs of Conventional HVAC system	=	Initial Costs+ PV of all Annual operating costs+PV of maintenance costs of year 5 +PV of maintenance costs of year 10 - PV of Scrap value @ 30 year end - PV of tax benefit on Depreciation for 10 years
	=	225000+22000/8%*(1-1/(1+8%)^30)+15000/(1+8%)^10+15000/(1+8%)^20-5000/(1+8%)^30-6750/8%*(1-1/(1+8%)^10
	=	437047.4
PV of Life time costs of Modified HVAC system	=	nitial Costs+ PV of all Annual operating costs+PV of maintenance costs of year 5 +PV of maintenance costs of year 10 - PV of Scrap value @ 30 year end - PV of tax benefit on Depreciation for 10 years
	=	300000+10000/8%*(1-1/(1+8%)^30)+4000/(1+8%)^10+4000/(1+8%)^20-5000/(1+8%)^30-9000/8%*(1-1/(1+8%)^10
	=	354401.2

.

Modified HVAC System Life Time Cost = $ 354,401.18

Conventional HVAC Systems Life Time Cost = $437,047.42

Savings = $82,646.24.

b) Assuming 1% rise in Operating costs Year on year, the PV Calculations would be as per below table. The 1% growth in Operating costs is factored in the PV of Annual operating costs.

PV of Life time costs of Conventional HVAC system	=	Initial Costs+ PV of all Annual operating costs+PV of maintenance costs of year 5 +PV of maintenance costs of year 10- PV of Scrap value at 30 year end- PV of tax benefit on Depreciation for 10 years
	=	225000+22000/(8%-1%)*(1-(1+1%)^30/(1+8%)^30)+15000/(1+8%)^10+15000/(1+8%)^20-5000/(1+8%)^30-6750/8%*(1-1/(1+8%)^10
	=	461564.71
PV of Life time costs of Modified HVAC system	=	nitial Costs+ PV of all Annual operating costs+PV of maintenance costs of year 5 +PV of maintenance costs of year 10 - PV of Scrap value @ 30 year end - PV of tax benefit on Depreciation for 10 years
	=	300000+10000/(8%-1%)*(1-(1+1%)^30/(1+8%)^30)+4000/(1+8%)^10+4000/(1+8%)^20-5000/(1+8%)^30-9000/8%*(1-1/(1+8%)^10
	=	365545.40

Due to increasing energy costs, the difference of NPV of competing systems will be as per below table

Scenario	PV of Conventional HVAC System	PV of Modified HVAC System
PV of Total Life Time Cost with increasing energy costs	461,564.71	365,545.40
PV of Total Life Time Cost without increasing energy costs	437,047.42	354,401.18
Difference in NPV of these competing systems	24,517.28	11,144.22

c) With every higher discounting rate, the PV of both systems would be lower and the difference would also be lower. But after 19% discounting rate the PV of Modified HVAC system will be higher than Conventional HVAC system. This is because the difference in initial cost incurred on Modified system would surpass the difference in PV of future outflows of Modified system over Conventional system.